Problem: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{k^2 + 20k + 100}{k^2 + 15k + 50}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 + 20k + 100}{k^2 + 15k + 50} = \dfrac{(k + 10)(k + 10)}{(k + 5)(k + 10)} $ Notice that the term $(k + 10)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k + 10)$ gives: $y = \dfrac{k + 10}{k + 5}$ Since we divided by $(k + 10)$, $k \neq -10$. $y = \dfrac{k + 10}{k + 5}; \space k \neq -10$